Chebyshev Polynomials
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The Chebyshev polynomial of degree
is
denoted
.
It is defined as:
![](I/ChebyshevPolynomials_files/image003.png)
Chebyshev polynomials satisfy the following relationships
and recursion formulae:
Recursion formulae:
![](I/ChebyshevPolynomials_files/image004.png)
![](I/ChebyshevPolynomials_files/image005.png)
![](I/ChebyshevPolynomials_files/image006.png)
Zeros, exactly
distinct zeros in the
interval
,
as follows:
![](I/ChebyshevPolynomials_files/image008.png)
Extrema, exactly
real extrema in the
interval
,
as follows:
![](I/ChebyshevPolynomials_files/image010.png)
![](I/ChebyshevPolynomials_files/image011.png)
Orthogonality:
![](I/ChebyshevPolynomials_files/image012.png)